Radial and angular correlations of doubly excited electrons

Abstract

The nature of electron correlations between two excited electrons is examined in terms of surface plots of charge-density distributions on suitably chosen planes. Initially the angular correlation is neglected such that charge distributions for singly and doubly excited states are displayed on the conventional (${r}_{1},{r}_{2}$) plane. It is shown that all singly excited states exhibit circular nodal lines on the (${r}_{1},{r}_{2}$) plane along $R={({r}_{1}^{2}+{r}_{2}^{2})}^{\frac{1}{2}}=\mathrm{const}$ and no radial nodal structure in the $\ensuremath{\alpha}=arctan(\frac{{r}_{1}}{{r}_{2}})$ coordinate, while doubly excited states are characterized by additional radial nodal structure. The interplay between angular and radial correlations is examined in terms of plots of surface charge density at each $R$ on the ($\ensuremath{\alpha},{\ensuremath{\theta}}_{12}$) plane for each channel. It is shown that channels which have attractive potential curves are characterized by large charge concentration for large ${\ensuremath{\theta}}_{12}$, while other channels which have less attractive or repulsive potentials are characterized by large charge concentration in the small-${\ensuremath{\theta}}_{12}$ region.